Let p1 and p2 denote the population proportions of males and females in the United States who answer, yes, definitely when asked whether they believe in miracles. Estimate these by going to the General Social Survey Web site (sda.berkeley.edu/GSS), selecting GSS with No Weight as the default weight selection, and then entering the variable MIRACLES for the rows, SEX for the columns, and YEAR (2008) as the selection filter.
a. Report point estimates of p1 and p2 .
b. Construct a 95% confidence interval for (p1 - p2), specifying the assumptions you make to use this method. Interpret.
c. Based on the interval in part b, explain why the proportion believing in miracles may have been quite a bit larger for females, or it might have been only moderately larger.